There are caricatures of math and the arts, and then there are characterizations, the best of which are accurate. Many students get dragged through the drudgery of mathematical algorithms and washout without ever seeing the beauty and creativity inherent in the discipline, so let's be a little more thorough and explore what philosophers have discovered about creativity. I'd argue that philosophers of mathematics are engaged in an entirely creative act like any sculptor is. The only difference is the medium.
In traditional concepts of mathematics and art, there are different underlying objects being studied. Mathematics focuses on the logic, direction, shape, quantity, and relations expressed in language, whereas art (which is a very broad term which has fine and commercial varieties) tends to refer to the novel expression of auditory and visual media, be it literature, poetry, paints, sculpture, music, and dance. In fact, there can be a lot of overlap depending on the interests of the thinker. I have a geometry textbook that relies heavily on the works of M.C. Escher to illustrate lessons. Is geometric tiling mathematics or art? Obviously both, with the difference arising from the methodology and aims of thinker. You say:
a lot of people seem to treat IQ as something unrelated to creativity
Many people do not see mathematics and logic as a creative venture, but I suspect that is more about how human beings are socialized (math drill! one-correct-logic!) than practicing. In philosophy, for instance, Imre Lakatos inspired by Karl Popper, someone famous for railing against scientific consensus regarding methodology, insisted mathematics was a creative endeavor. Certainly, if you read Polya's How to Solve It (GB), the text claims mathematics is a heuristic rather than algorithmic endeavor. This, in fact, is a common theme among the mathematically and scientifically inclined starting since the 1960's and the failure of the program of logical positivism. Paul Feyerabend wrote a book Against Method because he saw that at the fundamental core of thought, there is no algorithm, only heuristic. (A very important mathematical distinction.)
Having a high IQ is often a sign of seeing things in quickly and in a novel way. The Mensa entrance examination doesn't present anything in the way of conceptual challenge, but rather in seeing a solution or pattern with an overwhelming problem space. One could argue that solving one of Raven's Progressive Matrices is an act of creativity, because the human solves it generally by a flash of insight rather than a calculation. And if you plumb the depths of mathematical genius, you'll find that the great names created math, they didn't just follow a recipe to get to a solution. Nikolai Lobachevsky is immortal in math history because he created an alternative to the axioms of Euclid, not necessarily because he mastered them. Great math is not solving a calculus problem to pass a test, it's envisioning the fluxion or differential and creating the calculus to begin with. Any professional mathematician will tell you that they are engaged in a creative act.
The real question is, are the mechanisms that allow for creativity in the fine and commercial arts the same that are used in mathematics? If you believe in a psychometrician's claim about G factor, the answer is broadly, yes. Honestly, there is some dispute on what characterizes intelligence, and the one commonality between the positions embodied by positions like Spearman's, Gardner's MI theory, or Cattell and Horn's views is the invocation of creativity which is often conceived of assembling ideas, words, or other primitives like color and sound, in novel ways. Hence, creativity, while domain specific, has a permutational flavor in all domains.
In my own domain of computer science, N vs. NP is a question which is open and bears on the question of creativity. In the study of computational theory, questions like the Halting problem have rigorous proofs in mathematical logic that suggest that there are some truths, some proofs, and thus some ideas that are inescapably beyond algorithmic methods and rely on intuitions. The notion of effective computability explored by Alan Turing, a great mathematician and logician who helped found computer science, constructed a concept called an oracle machine precisely because even in rigorous math and logic, sometimes the only way to get there is through creative insights. Goedel talks about unprovable truth, and modern philosophy of mind is built around defeasibility (SEP) and non-monotonic logic (SEP). One of my motivations for persisting on this site is to spread the word that mathematics and computer science are more than algorithms and machines that run them.
The fact that your visual system creates color and doesn't discover it should give you pause about how deeply the act of creativity extends. Modern science and some modern philosophy, in fact, supports the idea that the entirety of conscious thought and perhaps the world as we understand it is an act of creativity at some level of the brain (IEP).